Linking Methods In Critical Point Theory

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Linking Methods in Critical Point Theory

Author : Martin Schechter
Publisher : Springer Science & Business Media
ISBN 13 : 146121596X
Total Pages : 305 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Linking Methods in Critical Point Theory by : Martin Schechter

Download or read book Linking Methods in Critical Point Theory written by Martin Schechter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the Trans-Canada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif ferential equations? To find out, read on ...

Critical Point Theory

Author : Martin Schechter
Publisher : Springer Nature
ISBN 13 : 303045603X
Total Pages : 347 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Critical Point Theory by : Martin Schechter

Download or read book Critical Point Theory written by Martin Schechter and published by Springer Nature. This book was released on 2020-05-30 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author’s own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied. Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book’s main subject: applications to problems in mathematics and physics. These include topics such as Schrödinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout. Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used.

Sign-Changing Critical Point Theory

Author : Wenming Zou
Publisher : Springer Science & Business Media
ISBN 13 : 0387766588
Total Pages : 288 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Sign-Changing Critical Point Theory by : Wenming Zou

Download or read book Sign-Changing Critical Point Theory written by Wenming Zou and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical points of a functional, they often cannot provide much-needed additional properties of these critical points. Sign-changing critical point theory has emerged as a new area of rich research on critical points of a differentiable functional with important applications to nonlinear elliptic PDEs. This book is intended for advanced graduate students and researchers involved in sign-changing critical point theory, PDEs, global analysis, and nonlinear functional analysis.

Critical Point Theory and Its Applications

Author : Wenming Zou
Publisher : Springer Science & Business Media
ISBN 13 : 0387329684
Total Pages : 323 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Critical Point Theory and Its Applications by : Wenming Zou

Download or read book Critical Point Theory and Its Applications written by Wenming Zou and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.

Minimax Methods in Critical Point Theory with Applications to Differential Equations

Author : Paul H. Rabinowitz
Publisher : American Mathematical Soc.
ISBN 13 : 0821807153
Total Pages : 110 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Minimax Methods in Critical Point Theory with Applications to Differential Equations by : Paul H. Rabinowitz

Download or read book Minimax Methods in Critical Point Theory with Applications to Differential Equations written by Paul H. Rabinowitz and published by American Mathematical Soc.. This book was released on 1986-07-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.

Critical Point Theory and Its Applications

Author : Wenming Zou
Publisher : Springer
ISBN 13 : 9780387329659
Total Pages : 318 pages
Book Rating : 4.3/5 (296 download)

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Book Synopsis Critical Point Theory and Its Applications by : Wenming Zou

Download or read book Critical Point Theory and Its Applications written by Wenming Zou and published by Springer. This book was released on 2006-06-13 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.

Minimax Systems and Critical Point Theory

Author : Martin Schechter
Publisher : Springer Science & Business Media
ISBN 13 : 0817649026
Total Pages : 239 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Minimax Systems and Critical Point Theory by : Martin Schechter

Download or read book Minimax Systems and Critical Point Theory written by Martin Schechter and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of self study. The new material covered also makes this book a must read for researchers in the theory of critical points.

Topics in Critical Point Theory

Author : Kanishka Perera
Publisher : Cambridge University Press
ISBN 13 : 110702966X
Total Pages : 171 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Topics in Critical Point Theory by : Kanishka Perera

Download or read book Topics in Critical Point Theory written by Kanishka Perera and published by Cambridge University Press. This book was released on 2013 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to critical point theory and shows how it solves many difficult problems.

Critical Point Theory in Global Analysis and Differential Topology

Author :
Publisher : Academic Press
ISBN 13 : 0080873456
Total Pages : 405 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Critical Point Theory in Global Analysis and Differential Topology by :

Download or read book Critical Point Theory in Global Analysis and Differential Topology written by and published by Academic Press. This book was released on 2014-05-14 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critical Point Theory in Global Analysis and Differential Topology

Abstract and Applied Analysis

Author : N. M. Chuong
Publisher : World Scientific
ISBN 13 : 981238944X
Total Pages : 579 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Abstract and Applied Analysis by : N. M. Chuong

Download or read book Abstract and Applied Analysis written by N. M. Chuong and published by World Scientific. This book was released on 2004 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material ? the coefficients may jump from domain to domain; Stochastic Analysis ? many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences

Handbook of Topological Fixed Point Theory

Author : Robert F. Brown
Publisher : Springer Science & Business Media
ISBN 13 : 9781402032219
Total Pages : 990 pages
Book Rating : 4.0/5 (322 download)

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Book Synopsis Handbook of Topological Fixed Point Theory by : Robert F. Brown

Download or read book Handbook of Topological Fixed Point Theory written by Robert F. Brown and published by Springer Science & Business Media. This book was released on 2005-07-21 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

Duality and Perturbation Methods in Critical Point Theory

Author : Nassif Ghoussoub
Publisher : Cambridge University Press
ISBN 13 : 9780521440257
Total Pages : 358 pages
Book Rating : 4.4/5 (42 download)

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Book Synopsis Duality and Perturbation Methods in Critical Point Theory by : Nassif Ghoussoub

Download or read book Duality and Perturbation Methods in Critical Point Theory written by Nassif Ghoussoub and published by Cambridge University Press. This book was released on 1993-08-19 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.

Critical Point Theory and Hamiltonian Systems

Author : Jean Mawhin
Publisher : Springer Science & Business Media
ISBN 13 : 1475720610
Total Pages : 292 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Critical Point Theory and Hamiltonian Systems by : Jean Mawhin

Download or read book Critical Point Theory and Hamiltonian Systems written by Jean Mawhin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN

Variational and Monotonicity Methods in Nonsmooth Analysis

Author : Nicuşor Costea
Publisher : Springer Nature
ISBN 13 : 3030816710
Total Pages : 450 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Variational and Monotonicity Methods in Nonsmooth Analysis by : Nicuşor Costea

Download or read book Variational and Monotonicity Methods in Nonsmooth Analysis written by Nicuşor Costea and published by Springer Nature. This book was released on 2021-09-20 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern and comprehensive presentation of a wide variety of problems arising in nonlinear analysis, game theory, engineering, mathematical physics and contact mechanics. It includes recent achievements and puts them into the context of the existing literature. The volume is organized in four parts. Part I contains fundamental mathematical results concerning convex and locally Lipschits functions. Together with the Appendices, this foundational part establishes the self-contained character of the text. As the title suggests, in the following sections, both variational and topological methods are developed based on critical and fixed point results for nonsmooth functions. The authors employ these methods to handle the exemplary problems from game theory and engineering that are investigated in Part II, respectively Part III. Part IV is devoted to applications in contact mechanics. The book will be of interest to PhD students and researchers in applied mathematics as well as specialists working in nonsmooth analysis and engineering.

Nonlinear Analysis, Differential Equations, and Applications

Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030725634
Total Pages : 791 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Nonlinear Analysis, Differential Equations, and Applications by : Themistocles M. Rassias

Download or read book Nonlinear Analysis, Differential Equations, and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2021-08-20 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers–Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg–Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdős-Rényi network model, strongly m-convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

Pfahlgründungen

Author : Dimitrios Kolymbas
Publisher :
ISBN 13 : 9780387512815
Total Pages : 169 pages
Book Rating : 4.5/5 (128 download)

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Book Synopsis Pfahlgründungen by : Dimitrios Kolymbas

Download or read book Pfahlgründungen written by Dimitrios Kolymbas and published by . This book was released on 1989 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Analysis - Theory and Methods

Author : Nikolaos S. Papageorgiou
Publisher : Springer
ISBN 13 : 3030034305
Total Pages : 577 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Nonlinear Analysis - Theory and Methods by : Nikolaos S. Papageorgiou

Download or read book Nonlinear Analysis - Theory and Methods written by Nikolaos S. Papageorgiou and published by Springer. This book was released on 2019-02-26 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.